There are seven Psalms that are specifically known for their entreaty for forgiveness (called “penitential psalms”). Psalm 102 is the fifth in the list (see also Psalms 6,32,38,51,130,143). It begins as do four other Psalms with a call to God to “hear my prayer” (see also Psalms 4, 17, 143).
The Psalmist is ill, and has been for some time. The illness, the Psalmist feels, is his own fault for his sins. He does not protest that he does not deserve his punishment. He only asks that God not take his life.
What I find most significant about all this is the focus of his prayer. Yes, it is certainly for himself. But more than that, it is for his nation, for the people of God. Jerusalem is reduced to rubble. That too for the sins of her inhabitants.
The illness of the writer then is a figure for the illness and distress of his people. Yet in his distress, his cry is for restoration – not of himself, but of his nation. He writes in anticipation of the day when someone will read his poem and take note that the Lord answered the man’s prayer for the restoration of Israel.
Please don’t make the mistake of confusing the nation of Israel with your own. God’s people are not of a particular national background. They are the Church. It would seem to me that the Church could stand a lot of prayer. Perhaps if we care enough about the Church to recognize its failings, we might pray change that, and ask God to restore to His people the glory it had in the beginning.